Modified Boltzmann approximation

Modified Boltzmann statistics is an approximation applicable to systems of $𝑁$ identical and indistinguishable particles at a high temperature with many accessible microstates so that it is unlikely for any two particles to be in the same quantum state. The canonical partition function is given by

𝑍 \approx ˜ 𝑍 𝑁! = (𝑍 1) 𝑁 𝑁!

where $˜ 𝑍$ is the canonical partition function given by Maxwell-Boltzmann statistics, and

𝑍 1 = \sum 𝑖 e x p (- 𝜀 𝑖 𝑘 𝐵 𝑇)

is the canonical partition function for a single particle.

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